Rinse and drain the black beans, then pat them dry with a paper towel to ensure a firm texture.
In a medium bowl, mash the black beans with a fork until mostly smooth but with some chunks remaining.
Finely dice the red bell pepper, red onion, and mince the garlic.
Add the egg, oat flour, nutritional yeast, diced vegetables, cumin, smoked paprika, sea salt, and black pepper to the beans.
Mix well and form into a thick patty; let it rest for 5 minutes to allow the oats to hydrate.
Heat the olive oil in a non-stick skillet over medium heat and sear the patty for 4-5 minutes per side until a golden crust forms.
While the burger cooks, whisk together the Greek yogurt, crumbled feta, and lime juice in a small bowl until creamy.
Toast the whole grain bun and assemble the burger by spreading the yogurt sauce on the bun and topping with the patty.